How to cite this paper
Torabi, K., Afshari, H & Heidari-Rarani, M. (2013). Free vibration analysis of a non-uniform cantilever Timoshenko beam with multiple concentrated masses using DQEM.Engineering Solid Mechanics, 1(1), 9-20.
Refrences
Bert, C.W., Malik, M. (1996). Differential quadrature method in computational mechanics: A review. Applied Mechanics Reviews, 49, 1-28.
Chen, C.N. (2001). Vibration of non-uniform shear deformable axisymmetric orthotropic circular plates solved by DQEM. Composite Structures, 53, 257-264.
Chen, C.N. (2002). DQEM vibration analyses of non-prismatic shear deformable beams resting on elastic foundations. Journal of Sound and Vibration, 255, 989-999.
Chen, C.N. (2005). DQEM analysis of in-plane vibration of curved beam structures. Advances in Engineering Software, 36, 412-424.
Chen, C.N. (2008). DQEM analysis of out-of-plane vibration of non-prismatic curved beam structures considering the effect of shear deformation. Advances in Engineering Software, 39, 466-472.
Chen, Y. (1963). On the vibration of beams or rods carrying a concentrated mass. Journal of Applied Mechanics, 30, 310-311.
De Rosa, M.A., Franciosi, C., & Maurizi, M.J. (1955). On the dynamics behavior of slender beams with elastic ends carrying a concentrated mass, Computers and Structures, 58, 1145-1159.
Du, H., Lim, M.K., Lin, & N.R. (1994). Application of generalized differential quadrature method to structural problems. International Journal for Numerical Methods in Engineering, 37, 1881-1896.
Du, H., Lim, M.K., & Lin, N.R. (1995). Application of generalized differential quadrature to vibration analysis. Journal of Sound and Vibration, 181, 279-293.
Gurgoze, M. (1984). A note on the vibrations of restrained beams and rods with point masses. Journal of Sound and Vibration, 96, 461-468.
Gurgoze, M. (1985). On the vibration of restrained beams and rods with heavy masses. Journal of Sound and Vibration, 100, 588-589.
Kaneko, T. (1975). On Timoshenko’s correction for shear in vibrating beams. Journal of Physics D: Applied Physics, 8, 1928-1937.
Karami, G., & Malekzadeh, P. (2002). A new differential quadrature methodology for beam analysis and the associated differential quadrature element method. Computer Methods in Applied Mechanics and Engineerig,191, 3509-3526.
Laura, P., Maurizi, M.J., & Pombo, J.L. (1975). A note on the dynamics analysis of an elastically restrained-free beam with a mass at the free end. Journal of Sound and Vibration, 41, 397-405.
Laura, P., Verniere de Irassar, P.L., & Ficcadenti, G.M. (1983). A note on transverse vibration of continuous beams subjected to an axial force and carrying concentrated masses, Journal of Sound and Vibration, 86, 279-284.
Lee, S.Y., & Lin, S.M. (1995). Vibration of elastically restrained non-uniform Timoshenko beams. Journal of Sound and Vibration, 183, 403-415.
Lin, R.M., Lim, M.K., & Du, H. (1994). Deflection of plates with nonlinear boundary supports using generalized differential quadrature. Computer and Structures, 53, 993-999.
Liu, W.H., Wu, J.R., & Huang, C.C. (1988). Free vibrations of beams with elastically restrained edges and intermediate concentrated masses. Journal of Sound and Vibration, 122, 193-207.
Malekzadeh, P., Karami, G., & Farid M. (2004). A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported. Computer Methods in Applied Mechanics and Engineering, 193, 4781-4796.
Rao, G.V., Saheb, K.M., & Janardhan, G.R. (2006), Fundamental frequency for large amplitude vibrations of uniform Timoshenko beams with central point concentrated mass using coupled displacement field method. Journal of Sound and Vibration, 298, 221-232.
Rossit, C.A., & Laura, P. (2001). Transverse vibrations of a cantilever beam with a spring mass system attached on the free end, Ocean Engineering, 28, 933-939.
Rossit, M.C.A., & Laura, P. (2001). Transverse normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end. Journal of the Acoustical Society of America, 110, 2837-2840.
Timoshenko, S., Young, D.H., & Weaver, W. (1974). Vibration problems in engineering. Wiley, New York.
Chen, C.N. (2001). Vibration of non-uniform shear deformable axisymmetric orthotropic circular plates solved by DQEM. Composite Structures, 53, 257-264.
Chen, C.N. (2002). DQEM vibration analyses of non-prismatic shear deformable beams resting on elastic foundations. Journal of Sound and Vibration, 255, 989-999.
Chen, C.N. (2005). DQEM analysis of in-plane vibration of curved beam structures. Advances in Engineering Software, 36, 412-424.
Chen, C.N. (2008). DQEM analysis of out-of-plane vibration of non-prismatic curved beam structures considering the effect of shear deformation. Advances in Engineering Software, 39, 466-472.
Chen, Y. (1963). On the vibration of beams or rods carrying a concentrated mass. Journal of Applied Mechanics, 30, 310-311.
De Rosa, M.A., Franciosi, C., & Maurizi, M.J. (1955). On the dynamics behavior of slender beams with elastic ends carrying a concentrated mass, Computers and Structures, 58, 1145-1159.
Du, H., Lim, M.K., Lin, & N.R. (1994). Application of generalized differential quadrature method to structural problems. International Journal for Numerical Methods in Engineering, 37, 1881-1896.
Du, H., Lim, M.K., & Lin, N.R. (1995). Application of generalized differential quadrature to vibration analysis. Journal of Sound and Vibration, 181, 279-293.
Gurgoze, M. (1984). A note on the vibrations of restrained beams and rods with point masses. Journal of Sound and Vibration, 96, 461-468.
Gurgoze, M. (1985). On the vibration of restrained beams and rods with heavy masses. Journal of Sound and Vibration, 100, 588-589.
Kaneko, T. (1975). On Timoshenko’s correction for shear in vibrating beams. Journal of Physics D: Applied Physics, 8, 1928-1937.
Karami, G., & Malekzadeh, P. (2002). A new differential quadrature methodology for beam analysis and the associated differential quadrature element method. Computer Methods in Applied Mechanics and Engineerig,191, 3509-3526.
Laura, P., Maurizi, M.J., & Pombo, J.L. (1975). A note on the dynamics analysis of an elastically restrained-free beam with a mass at the free end. Journal of Sound and Vibration, 41, 397-405.
Laura, P., Verniere de Irassar, P.L., & Ficcadenti, G.M. (1983). A note on transverse vibration of continuous beams subjected to an axial force and carrying concentrated masses, Journal of Sound and Vibration, 86, 279-284.
Lee, S.Y., & Lin, S.M. (1995). Vibration of elastically restrained non-uniform Timoshenko beams. Journal of Sound and Vibration, 183, 403-415.
Lin, R.M., Lim, M.K., & Du, H. (1994). Deflection of plates with nonlinear boundary supports using generalized differential quadrature. Computer and Structures, 53, 993-999.
Liu, W.H., Wu, J.R., & Huang, C.C. (1988). Free vibrations of beams with elastically restrained edges and intermediate concentrated masses. Journal of Sound and Vibration, 122, 193-207.
Malekzadeh, P., Karami, G., & Farid M. (2004). A semi-analytical DQEM for free vibration analysis of thick plates with two opposite edges simply supported. Computer Methods in Applied Mechanics and Engineering, 193, 4781-4796.
Rao, G.V., Saheb, K.M., & Janardhan, G.R. (2006), Fundamental frequency for large amplitude vibrations of uniform Timoshenko beams with central point concentrated mass using coupled displacement field method. Journal of Sound and Vibration, 298, 221-232.
Rossit, C.A., & Laura, P. (2001). Transverse vibrations of a cantilever beam with a spring mass system attached on the free end, Ocean Engineering, 28, 933-939.
Rossit, M.C.A., & Laura, P. (2001). Transverse normal modes of vibration of a cantilever Timoshenko beam with a mass elastically mounted at the free end. Journal of the Acoustical Society of America, 110, 2837-2840.
Timoshenko, S., Young, D.H., & Weaver, W. (1974). Vibration problems in engineering. Wiley, New York.